Heat vegetable oil in a large skillet over medium heat.
Add the shredded chicken, chili powder, and cumin, stirring for 2 minutes to incorporate spices.
Add the black beans and salsa to the chicken mixture, stirring for 3 minutes until the liquid is slightly reduced and the mixture is hot.
Warm the flour tortillas in a microwave for 20 seconds or on a dry skillet for 15 seconds per side until pliable.
Place 1/4 cup of cooked rice in the center of each tortilla.
Top the rice with 1/4 of the chicken and bean mixture, followed by 1/4 cup of shredded cheese.
Fold the left and right sides of the tortilla toward the center, then roll tightly from the bottom to the top.
Place the burritos seam-side down in a hot skillet for 1 to 2 minutes per side until the tortilla is golden and the cheese is fully melted.